Endoscopic features of gastro-intestinal lymphomas: From diagnosis to follow-up

Many progresses have been done in the management of gastrointestinal(GI) lymphomas during last decades, especially after the discovery of Helicobacter pylori-dependent lymphoma development. The stepwise implementation of new endoscopic techniques, by means of echoendoscopy or double-balloon enteroscopy, enabled us to more precisely describe the endoscopic features of GI lymphomas with substantial contribution in patient management and in tailoring the treatment strategy with organ preserving approaches. In this review, we describe the recent progresses in GI lymphoma management from disease diagnosis to follow-up with a specific focus on the endoscopic presentation according to the involved site and the lymphoma subtype. Additionally, new or emerging endoscopic technologies that have an impact on the management of gastrointestinal lymphomas are reported. We here discuss the two most common subtypes of GI lymphomas: the mucosaassociated lymphoid tissue and the diffuse large B cell lymphoma. A general outline on the state-of-the-art of the disease and on the role of endoscopy in both diagnosis and follow-up will be performed.

Rare gastrointestinal lymphomas: the endoscopic investigation

Gastrointestinal lymphomas represent up to 10%of gastrointestinal malignancies and about one third of nonHodgkin lymphomas.The most prominent histologies are mucosa-associated lymphoid tissue lymphoma and diffuse large B-cell lymphoma.However,the gastrointestinal tract can be the site of rarer lymphoma subtypes as a primary or secondary localization.Due to their rarity and the multifaceted histology,an endoscopic classification has not been validated yet.This review aims to analyze the endoscopic presentation of rare gastrointestinal lymphomas from disease diagnosis to follow-up,according to the involved site and lymphoma subtype.Existing,new and emerging endoscopic technologies have been examined.In particular,we investigated the diagnostic,prognostic and follow-up endoscopic features of T-cell and natural killer lymphomas,lymphomatous polyposis and mantle cell lymphoma,follicular lymphoma,plasma cell related disease,gastrointestinal lymphomas in immunodeficiency and Hodgkin’s lymphoma of the gastrointestinal tract.Contrarily to more frequent gastrointestinal lymphomas,data about rare lymphomas are mostly extracted from case series and case reports.Due to the data paucity,a synergism between gastroenterologists and hematologists is required inorder to better manage the disease.Indeed,clinical and prognostic features are different from nodal and extranodal or the bone marrow(in case of plasma cell disease)counterpart.Therefore,the approach should be based on the knowledge of the peculiar behavior and natural history of disease.

FIXED POINTS OF α-TYPE F-CONTRACTIVE MAPPINGS WITH AN APPLICATION TO NONLINEAR FRACTIONAL DIFFERENTIAL EQUATION

In this paper, we introduce new concepts of a-type F-contractive mappings which are essentially weaker than the class of F-contractive mappings given in [21, 22] and different from a-GF-contractions given in [8]. Then, sufficient conditions for the existence and uniqueness of fixed point are established for these new types of contractive mappings, in the setting of complete metric space. Consequently, the obtained results encompass various generalizations of the Banach contraction principle. Moreover, some examples and an application to nonlinear fractional differential equation are given to illustrate the usability of the new theory.

EDELSTEIN-SUZUKI-TYPE RESULTS FOR SELF-MAPPINGS IN VARIOUS ABSTRACT SPACES WITH APPLICATION TO FUNCTIONAL EQUATIONS

The fixed point theory provides a sound basis for studying many problems in pure and applied sciences. In this paper, we use the notions of sequential compactness and completeness to prove Eldeisten-Suzuki-type fixed point results for self-mappings in various abstract spaces. We apply our results to get a bounded solution of a functional equation arising in dynamic programming.

LANDESMAN-LAZER TYPE (p,q)-EQUATIONS WITH NEUMANN CONDITION

We consider a Neumann problem driven by the(p,g)-Laplacian under the Landesman-Lazer type condition.Using the classical saddle point theorem and other classical results of the calculus of variations,we show that the problem has at least one nontrivial weak solution.

ON NONCOERCIVE (p,q)-EQUATIONS

We consider a nonlinear Dirichlet problem driven by a(p,q)-Laplace differential operator(1<q<p).The reaction is(p-1)-linear near±∞and the problem is noncoercive.Using variational tools and truncation and comparison techniques together with critical groups,we produce five nontrivial smooth solutions all with sign information and ordered.In the particular case when q=2,we produce a second nodal solution for a total of six nontrivial smooth solutions all with sign information.

HOMOCLINIC SOLUTIONS OF NONLINEAR LAPLACIAN DIFFERENCE EQUATIONS WITHOUT AMBROSETTI-RABINOWITZ CONDITION

The aim of this paper is to establish the existence of at least two non-zero homoclinic solutions for a nonlinear Laplacian difference equation without using AmbrosettiRabinowitz type-conditions. The main tools are mountain pass theorem and Palais-Smale compactness condition involving suitable functionals.

MEIR-KEELER TYPE CONTRACTIONS FOR TRIPLED FIXED POINTS

In 2011, Berinde and Borcut [6] introduced the notion of tripled fixed point in partially ordered metric spaces. In our paper, we give some new tripled fixed point theorems by using a generalization of Meir-Keeler contraction：

COMMON FIXED POINT THEOREMS FOR MULTI-VALUED MAPS

We establish some results on coincidence and common fixed points for a twopair of multi-valued and single-valued maps in complete metric spaces. Presented theorems generalize recent results of Gordji et al [4] and several results existing in the literature.