AN EXISTENCE THEOREM OF POSITIVE SOLUTIONS FOR ELASTIC BEAM EQUATION WITH BOTH FIXED END-POINTS

By using the degree theory on cone an existence theorem of positive solution for a class of fourth-order two-point BVP's is obtained. This class of BVP's usually describes the deformation of the elastic beam with both fixed end-points.

ON A FIXED POINT THEOREM IN 2-BANACH SPACES AND SOME OF ITS APPLICATIONS

The aim of this article is to prove a fixed point theorem in 2-Banach spaces and show its applications to the Ulam stability of functional equations. The obtained stability re- sults concern both some single variable equations and the most important functional equation in several variables, namely, the Cauchy equation. Moreover, a few corollaries corresponding to some known hyperstability outcomes are presented.

SOME NEW EXTENSIONS OF EDELSTEIN-SUZUKI-TYPE FIXED POINT THEOREM TO G-METRIC AND G-CONE METRIC SPACES

In this paper, we prove some fixed point theorems for generalized contractions in the setting of G-metric spaces. Our results extend a result of Edelstein [M. Edelstein, On fixed and periodic points under contractive mappings, J. London Math. Soc., 37 （1962）, 74-79] and a result of Suzuki [T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 （2009）, 5313-5317]. We prove, also, a fixed point theorem in the setting of G-cone metric spaces.

FIXED POINT THEOREMS FOR MEIR-KEELER CONDENSING OPERATORS VIA MEASURE OF NONCOMPACTNESS

In this article, we introduce the notion of Meir-Keleer condensing operator in a Banach space, a characterization using L-functions and provide a few generalization of Darbo fixed point theorem. Also, we introduce the concept of a bivariate Meir-Keleer condensing operator and prove some coupled fixed point theorems. As an application, we prove the existence of solutions for a large class of functional integral equations of Volterra type in two variables.

More on Fixed Point Theorem of{a,b,c}-Generalized Nonexpansive Mappings in Normed Spaces

Let X be a weakly Cauchy normed space in which the parallelogram law holds,C be a bounded closed convex subset of X with one contracting point and T be an{a,b,c}-generalized-nonexpansive mapping from C into C.We prove that the infimum of the set{‖x-T(x)‖}on C is zero,study some facts concerning the{a,b,c}-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to C is singleton.Depending on the fact that the{a,b,0}-generalized-nonexpansive mapping from C into C has fixed points,accord-ingly,another version of the Browder's strong convergence theorem for mappings is given.

Common Fixed Point Theorems of Single-valued and Set-valued Mappings in Complete,Convex Metric Spaces

Under the conditions of compatility or sub -c ompatility between a sigle-valued mapping and set-valued mapping, this paper d iscusses the existence of common fixed points for two set-valued mappings and a single-valued mapping in complete, convex matric spaces. We extend and develop the main results.

NEW COLLECTIVELY FIXED POINT THEOREMS AND APPLICATIONS IN G-CONVEX SPACES

By applying the technique of continuous partition of unity and Tychonoff's fixed point theorem,. some new collectively fixed point theorems for a family of set-valued, mappings defined on the product space of noncompact G-convex spaces are proved. As applications, some nonempty intersetion theorems of Ky Fan type for a family of subsets of the product space of G convex spaces are proved; An existence theorem of solutions for a system of nonlinear inequalities is given in G-convex spaces and some equilibrium existence of abstract economies are also obtained in G convex spaces. Our theorems theorems of improve, unify and generalized many important known results in recent literature.

NEW FIXED POINT THEOREMS FOR P_1-COMPACT MAPPINGS IN BANACH SPACES

E E. Browder and W. V. Petryshyn defined the topological degree for A- proper mappings and then W. V. Petryshyn studied a class of A-proper mappings, namely, P1-compact mappings and obtained a number of important fixed point theorems by virtue of the topological degree theory. In this paper, following W. V. Petryshyn, we continue to study P1-compact mappings and investigate the boundary condition, under which many new fixed point theorems of P1-compact mappings are obtained. On the other hand, this class of A-proper mappings with the boundedness property includes completely continuous operators and so, certain interesting new fixed point theorems for completely continuous operators are obtained immediately. As a result of it, our results generalize several famous theorems such as Leray-Schauder＇s theorem, Rothe＇s theorem, Altman＇s theorem, Petryshyn＇s theorem, etc.

Common Fixed Point Theorem in Intuitionistic Fuzzy Metric Space Using <i>R</i>-Weakly Commuting Mappings

In this paper, we prove a common fixed point theorem in Intuitionistic fuzzy metric space by using pointwise R-weak commutativity and reciprocal continuity of mappings satisfying contractive conditions.

ON NEW APPROXIMATIONS FOR GENERALIZED CAUCHY FUNCTIONAL EQUATIONS USING BRZDȨK AND CIEPLIŃSKI'S FIXED POINT THEOREMS IN 2-BANACH SPACES

In this work,we apply the Brzdȩk and Ciepliński's fixed point theorem to investigate new stability results for the generalized Cauchy functional equation of the form f(ax+by)=af(x)+bf(y),where a,b∈N and f is a mapping from a commutative group(G,+)to a 2-Banach space(Y,||·,·||).Our results are generalizations of main results of Brzdȩk and Ciepliński[J Brzdȩk,K Ciepliński.On a fixed point theorem in 2-normed spaces and some of its applications.Acta Mathematica Scientia,2018,38B(2):377-390].

SET-VALUED CARISTI’S FIXED POINT THEOREM AND EEELAND’S VARIATIONAL PRINCIPLE

This paper proposes a formally stronger set-valued Caristi’s fixed point theorem and by using a simple method we give a direct proof for the equivalence between Ekeland’s variational principle and this set-valued Caristi’s fixed point theorem.The results stated in this paper improve and strengthen the corresponding results in[4].

Rothe’s Fixed Point Theorem and the Controllability of the Benjamin-Bona-Mahony Equation with Impulses and Delay

For many control systems in real life, impulses and delays are intrinsic phenomena that do not modify their controllability. So we conjecture that under certain conditions the abrupt changes and delays as perturbations of a system do not destroy its controllability. There are many practical examples of impulsive control systems with delays, such as a chemical reactor system, a financial system with two state variables, the amount of money in a market and the savings rate of a central bank, and the growth of a population diffusing throughout its habitat modeled by a reaction-diffusion equation. In this paper we apply the Rothe’s Fixed Point Theorem to prove the interior approximate controllability of the following Benjamin Bona-Mohany(BBM) type equation with impulses and delay where and are constants, Ω is a domain in , ω is an open non-empty subset of Ω , denotes the characteristic function of the set ω , the distributed control , are continuous functions and the nonlinear functions are smooth enough functions satisfying some additional conditions.

A Generalization of Caristi Fixed Point Theorem

Let X be a metric space with an ordering structure,A: X→X is a operator and x≤Ax for any x∈X. In this paper we prove a new fixed point theorem, which generalizes famous caristi fixed point theorem.

Traversable Wormholes and the Brouwer Fixed-Point Theorem

The Brouwer fixed-point theorem in topology states that for any continuous mapping f on a compact convex set into itself admits a fixed point, i.e., a point x0 such that f(x0) = x0. Under suitable conditions, this fixed point corresponds to the throat of a traversable wormhole, i.e., b(r0) = r0 for the shape function b = b(r). The possible existence of wormholes can therefore be deduced from purely mathematical considerations without going beyond the existing physical requirements.

GENERALIZED MINIMAX INEQUALITIES AND FIXED POINT THEOREMS

Recently many authors have generalized the famous Ky Fan's minimax inequality. In this paper, we put forward T-diagonal convexity (concavity) conditions and develop the main results in this respect. Next, we discuss some fixed point problems, and generalize the Fan-Glicksberg's fixed point theorem[14].

New Fixed Point Results of Generalized g-Quasi-Contractions in Cone b-Metric Spaces Over Banach Algebras

In this paper, we introduce the concept of generalized g-quasi-contractions in the setting of cone b-metric spaces over Banach algebras. By omitting the assump- tion of normality we establish common fixed point theorems for the generalized g- quasi-contractions with the spectral radius r（λ） of the g-quasi-contractive constant vector λ satisfying r（λ） ∈[0,1） in the setting of cone b-metric spaces over Banach al- gebras, where the coefficient s satisfies s ≥ 1. The main results generalize, extend and unify several well-known comparable results in the literature.

FIXED POINT THEOREMS AND BEST APPROXIMATION IN CONVEX METRIC SPACES

Results regarding best approximation and best Simultaneous approximation on convex metric spaces are Obtained.Existence of fixed points for an ultimately nonexpansive semigroup of mappings is also shown.

CARISTI TYPE HYBRID FIXED POINT THEOREMS IN MENGERPROBABILISTIC METRIC SPACE

This paper brings forward the concept of Caristi type hybrid fixed point in M-PM-space, by giving two hybrid fixed point theorems and two common hybrid fixed point theorems of sequences of set-valued mappings, the theorems improve and generalize the Caristi's fixed point and correspond to recent important results.

FIXED POINT INDEX OF UNIFORM LIMIT OF SET-VALUED STRICT SET-CONTRACTIVE MAPPINGS AND ITS APPLICATIONS

In this paper, the class of uniform limit mappings of set-valued, strick set-contractive mappings is discussed. Furthermore, the fixed point index theory for the uniform limit mappings is established. Using the fixed point index theory, some positive fixed point theorems are proved. Our theorems generalize some results in [1,4,5,7].

Fixed Point Theory for 1-Set Weakly Contractive Operators in Banach Spaces

In this work, using an analogue of Sadovskii＇s fixed point result and several important inequalities we investigate and give new existence theorems for the nonlinear operator equation F（x） =μx, （μ≥1） for some weakly sequentially continuous, weakly condensing and weakly 1-set weakly contractive operators with different boundary conditions. Correspondingly, we can obtain some applicable fixed point theorems of Leray-Schauder, Altman and Furi-Pera types in the weak topology setting which generalize and improve the corresponding results of [3,15,16].