A NEW ITERATIVE METHOD FOR FINDING COMMON SOLUTIONS OF GENERALIZED EQUILIBRIUM PROBLEM,FIXED POINT PROBLEM OF INFINITE k-STRICT PSEUDO-CONTRACTIVE MAPPINGS,AND QUASI-VARIATIONAL INCLUSION PROBLEM

In this article, we introduce a hybrid iterative scheme for finding a common element of the set of solutions for a generalized equilibrium problems, the set of common fixed point for a family of infinite k-strict pseudo-contractive mappings, and the set of solutions of the variational inclusion problem with multi-valued maximal monotone mappings and inverse-strongly monotone mappings in Hilbert space. Under suitable conditions, some strong convergence theorems are proved. Our results extends the recent results in G.L.Acedo and H.K.Xu [2], Zhang, Lee and Chan [8], Wakahashi and Toyoda [9], Takahashi and Takahashi [I0] and S. S. Chang, H. W. Joseph Lee and C. K. Chan [II], S.Takahashi and W.Takahashi [12]. Moreover, the method of proof adopted in this article is different from those of [4] and [12].

Uniqueness of Common Fixed Points for a Family of Mappings with <i>Φ</i>-Contractive Condition in 2-Metric Spaces

In this paper, we will introduce a class of 5-dimensional functions Φ and prove that a family of self-mappings {Ti,j} iεN in 2-metric space have an unique common fixed point if 1) {Ti,j} iεN satisfies Φj-contractive condition, where ΦjεΦ, for each jεN;2) Tm,μ n,v for all m,n,μ,vεN with μ ≠ v . Our main result generalizes and unifies many known unique common fixed point theorems in 2-metric spaces.

APPROXIMATION OF FIXED POINTS AND VARIATIONAL SOLUTIONS FOR PSEUDO-CONTRACTIVE MAPPINGS IN BANACH SPACES

Let K be a nonempty, closed and convex subset of a real reflexive Banach space E which has a uniformly Gateaux differentiable norm. Assume that every nonempty closed con- vex and bounded subset of K has the fixed point property for nonexpansive mappings. Strong convergence theorems for approximation of a fixed point of Lipschitz pseudo-contractive map- pings which is also a unique solution to variational inequality problem involving φ-strongly pseudo-contractive mappings are proved. The results presented in this article can be applied to the study of fixed points of nonexpansive mappings, variational inequality problems, con- vex optimization problems, and split feasibility problems. Our result extends many recent important results.

CONVERGENCE OF ISHIKAWA TYPE ITERATIVE SEQUENCE WITH ERRORS FOR QUASI-CONTRACTIVE MAPPINGS IN CONVEX METRIC SPACES

Some convergence theorems of Ishikawa type iterative sequence with errors for nonlinear general quasi-contractive mapping in convex metric spaces are proved. The results not only extend and improve the corresponding results of L. B. Ciric, Q. H. Liu, H. E. Rhoades and H. K. Xu, et al., but also give an affirmative answer to the open question of Rhoades-Naimpally- Singh in convex metric spaces.

Unique Common Fixed Points for Two Weakly C~*-contractive Mappings on Partially Ordered 2-metric Spaces

In this paper, we give existence theorems of common fixed points for two mappings with a weakly C*-contractive condition on partially ordered 2-metric spaces and give a sufficient condition under which there exists a unique common fixed point.

Coupled Fixed Point for (<i>&alpha;</i>, <i>&Psi;</i>)-Contractive in Partially Ordered Metric Spaces Using Compatible Mappings

In this paper, first we introduce notions of (α, Ψ)-contractive and (α)-admissible for a pair of map and prove a coupled coincidence point theorem for compatible mappings using these notions. Our work extends and generalizes the results of Mursaleen et al. [1]. At the end, we will provide an example in support of our result.

ESTIMATE ON THE BLOCH CONSTANT FOR CERTAIN HARMONIC MAPPINGS UNDER A DIFFERENTIAL OPERATOR

In this paper,we first obtain the precise values of the univalent radius and the Bloch constant for harmonic mappings of the formL(f)=zfz-zfz,where f represents normalized harmonic mappings with bounded dilation.Then,using these results,we present better estimations for the Bloch constants of certain harmonic mappings L(f),where f is a K-quasiregular harmonic or open harmonic.Finally,we establish three versions of BlochLandau type theorem for biharmonic mappings of the form L(f).These results are sharp in some given cases and improve the related results of earlier authors.

ON THE UNIVALENCE OF CERTAIN POLYHARMONIC MAPPINGS WITH BOUNDED LENGTH DISTORTIONS

The main purpose of this paper is to investigate the univalence of normalized polyharmonic mappings with bounded length distortions in the unit disk.We first establish the coefficient estimates for polyharmonic mappings with bounded length distortions.Then,using these results,we establish five Landau-type theorems for subclasses of polyharmonic mappings F and L(F),where F has bounded length distortion and L is a differential operator.

Leveraging ROTI map derived from Indonesian GNSS receiver network for advancing study of Equatorial Plasma Bubble in Southeast/East Asia

This paper highlights the crucial role of Indonesia’s GNSS receiver network in advancing Equatorial Plasma Bubble(EPB)studies in Southeast and East Asia,as ionospheric irregularities within EPB can disrupt GNSS signals and degrade positioning accuracy.Managed by the Indonesian Geospatial Information Agency(BIG),the Indonesia Continuously Operating Reference Station(Ina-CORS)network comprises over 300 GNSS receivers spanning equatorial to southern low-latitude regions.Ina-CORS is uniquely situated to monitor EPB generation,zonal drift,and dissipation across Southeast Asia.We provide a practical tool for EPB research,by sharing two-dimensional rate of Total Electron Content(TEC)change index(ROTI)derived from this network.We generate ROTI maps with a 10-minute resolution,and samples from May 2024 are publicly available for further scientific research.Two preliminary findings from the ROTI maps of Ina-CORS are noteworthy.First,the Ina-CORS ROTI maps reveal that the irregularities within a broader EPB structure persist longer,increasing the potential for these irregularities to migrate farther eastward.Second,we demonstrate that combined ROTI maps from Ina-CORS and GNSS receivers in East Asia and Australia can be used to monitor the development of ionospheric irregularities in Southeast and East Asia.We have demonstrated the combined ROTI maps to capture the development of ionospheric irregularities in the Southeast/East Asian sector during the G5 Geomagnetic Storm on May 11,2024.We observed simultaneous ionospheric irregularities in Japan and Australia,respectively propagating northwestward and southwestward,before midnight,whereas Southeast Asia’s equatorial and low-latitude regions exhibited irregularities post-midnight.By sharing ROTI maps from Indonesia and integrating them with regional GNSS networks,researchers can conduct comprehensive EPB studies,enhancing the understanding of EPB behavior across Southeast and East Asia and contributing significantly to ionospheric research.

Stability analysis of approximately multidimensional additive mappings on fuzzy spaces

The intention of this paper is to study new additive kind multi-dimensional functional equations inspired by several applications of difference equations in biology,control theory,economics,and computer science,as well as notable implementation of fuzzy ideas in certain situations involving ambiguity or vagueness.In the context of different fuzzy spaces,we demonstrate their various fundamental stabilities related to Ulam stability theory.An appropriate example is given to show how stability result fails when the singular case occurs.The findings of this study suggest that stability results are valid in situations with uncertain or imprecise data.The stability results obtained under these fuzzy spaces are compared with previous stability results.

HB-Continuous Mappings in L-Topological Space

In this paper, we introduce and study the notion of HB-closed sets in L-topological space. Then, HB-convergence theory for L-molecular nets and L-ideals is established in terms of HB-closedness. Finally, we give a new definition of fuzzy H-continuous [1] which is called HB-continuity on the basis of the notion of H-bounded L-subsets in L-topological space. Then we give characterizations and properties by making use of HB-converges theory of L-molecular nets and L-ideals.

A New Kind of Pre-Mean-Type Mappings and Its Gauss Iteration

A function which is reflexive is called by pre-mean, a more generalized definition of a mean. In this paper, we define a new pre-mean and study its properties, and then using the given invariant curve we consider the problem of convergence of Gauss iteration of a kind of pre-mean type mappings generated by the exponential and logarithmic functions.

SOME CONVERGENCE PROBLEM OF ITERATIVE SEQUENCESFOR ACCRETIVE AND PSEUDO-CONTRACTIVETYPE MAPPING IN BANACH SPACES

Some necessary and sufficient conditions for convergence of Ishikawa Mann and steepest descent iterative sequence for accretive and pseudo-contractive type mapping in Banach spaces were obtained. The results improve, extend and include some recent results.

G-Contractive Sequential Composite Mapping Theorem in Banach or Probabilistic Banach Space and Application to Prey-Predator System and A &H Stock Prices

Theorems of iteration g-contractive sequential composite mapping and periodic mapping in Banach or probabilistic Bannach space are proved, which allow some contraction ratios of the sequence of mapping might be larger than or equal to 1, and are more general than the Banach contraction mapping theorem. Application to the proof of existence of solutions of cycling coupled nonlinear differential equations arising from prey-predator system and A&H stock prices are given.

Iterative Processes with Errors for Generalized Set-Valued φ-Hemi-contractive Mapping in Banach Spaces

A new conception of generalized set-valued Ф-hemi-contractive mapping in Banach spaces is presented. Some strong convergence theorems of Ishikawa and Mann iterative approximation with errors is proved. The results in this paper improve and extend the earlier results.

A Note on the Paper “Generalized -Contraction for a Pair of Mappings on Cone Metric Spaces”

We note that Theorem 2.3 [1] is a consequence of the same theorem for one map.

Landslide Susceptibility Mapping Using RBFN-Based Ensemble Machine Learning Models

This study was aimed to prepare landslide susceptibility maps for the Pithoragarh district in Uttarakhand,India,using advanced ensemble models that combined Radial Basis Function Networks(RBFN)with three ensemble learning techniques:DAGGING(DG),MULTIBOOST(MB),and ADABOOST(AB).This combination resulted in three distinct ensemble models:DG-RBFN,MB-RBFN,and AB-RBFN.Additionally,a traditional weighted method,Information Value(IV),and a benchmark machine learning(ML)model,Multilayer Perceptron Neural Network(MLP),were employed for comparison and validation.The models were developed using ten landslide conditioning factors,which included slope,aspect,elevation,curvature,land cover,geomorphology,overburden depth,lithology,distance to rivers and distance to roads.These factors were instrumental in predicting the output variable,which was the probability of landslide occurrence.Statistical analysis of the models’performance indicated that the DG-RBFN model,with an Area Under ROC Curve(AUC)of 0.931,outperformed the other models.The AB-RBFN model achieved an AUC of 0.929,the MB-RBFN model had an AUC of 0.913,and the MLP model recorded an AUC of 0.926.These results suggest that the advanced ensemble ML model DG-RBFN was more accurate than traditional statistical model,single MLP model,and other ensemble models in preparing trustworthy landslide susceptibility maps,thereby enhancing land use planning and decision-making.

CQ Method for Strictly Pseudo-Contractive Mapping

This paper obtains a strong convergence theorem for k-strictly pseudo-contractive mapping under the framework of Hilbert spaces using CQ method. Due to the fact that non-expansive mapping is only O-strictly pseudo-contractive, the main result obtained in this paper extends the corresponding main result of Nakajo-Takahashi from non-expansive mapping to k-strictly pseudo-contractive one, where k∈ [0,1）.

Hybrid Extragradient-Type Methods for Finding a Common Solution of an Equilibrium Problem and a Family of Strict Pseudo-Contraction Mappings

This paper proposes a new hybrid variant of extragradient methods for finding a common solution of an equilibrium problem and a family of strict pseudo-contraction mappings. We present an algorithmic scheme that combine the idea of an extragradient method and a successive iteration method as a hybrid variant. Then, this algorithm is modified by projecting on a suitable convex set to get a better convergence property. The convergence of two these algorithms are investigated under certain assumptions.

Compiling molecular evidence from a tetraploid rose genome into a near-saturated map for the identification of pigment-related genes

With their high economic value and cultural significance,modern roses are one of the most important ornamental plants.Because of their complicated genetic background and tetraploid nature,the creation of high-density genetic maps of roses has been a challenge that has slowed the pace of molecular breeding for modern roses.The current construction of tetraploid genetic maps based on existing diploid rose genomes could lead to inaccurate marker information and genotyping results.Therefore,we generated the first high-quality tetraploid genome of Rosa chinensis‘Yunzheng Xiawei.'Utilizing Illumina,PacBio,and Hi-C sequencing technologies,we assembled a genome of 858.59 Mb with 14pseudo-chromosomes.Mode of inheritance analysis using PolyOrigin indicated that modern roses show both quadrivalent and bivalent pairing.Based on this reference genome,high-density genetic maps were constructed using MSTmap with nearly saturated markers.Quantitative trait locus(QTL)analysis was conducted using WinQTLCart and R/qtl for flavonoids and carotenoids,and 11 QTL clusters were identified.By combining the genome annotation,phylogenetic analyses,and gene expression analyses,we were able to identify several key genes related to flavonoid and carotenoid biosynthesis.This study provides the basis for further genetic analyses of highly heterozygous tetraploid roses and could facilitate the progress of marker-assisted selection in modern roses.