Zamfirescu mappings under Pata-type condition: Results and application to an integral equation

Introduction/purpose: Pata-type and Zamfirescu mappings are extended beyond metric spaces. Methods: The concept of Pata-type Zamfirescu mapping within the framework of S-metric spaces is employed. Results: A series of corresponding outcomes has been established. Furthermore, the obtained results are employed to solve an integral equation. Conclusions: S-Pata type and Zamfirescu mappings have unique fixed points.Preslikavanja tipa Pata i Zamfiresku su proširena izvan metričkih prostora. Metode: Primenjen je koncept Zamfiresku preslikavanja tipa Pata u okviru S-metričkih prostora. Rezultati: Utvrđen je niz odgovarajućih ishoda. Zatim su se dobijeni rezultati koristili za rešavanje integralne jednačine. Zaključak: Preslikavanja tipa S-Pata i Zamfiresku imaju jedinstvene nepokretne tačke

A QUADRUPLE COMMON FIXED POINT THEOREMS IN G b -METRIC SPACES

In this paper, we prove a quadruple common fixed point theorem in G b -metric space and some results are also given as corollaries. The results obtained are verified with the help of examples

Fixed point results for β - F-weak contraction mappings in complete S-metric spaces

U ovom radu uvodi se pojam β - F-slabe kontrakcije koristeći koncepte F-slabe kontrakcije i a - ps-kontrakcije. Metode: Korišćenjem b-F-slabe kontrakcije dokazuju se neke teoreme o fiksnim tačkama u okviru S-metričkih prostora. Rezultati: Dobijeni rezultati o fiksnim tačkama u S-metričkim prostorima generalizuju neke poznate rezultate u literaturi. Zaključak: β - F-slaba kontrakcija generalizuje neke važne tipove kontrakcija i ispituje postojanje fiksne tačke u S-metričkim prostorima. Rezultati se koriste za rešavanje nelinearne Fredholmove integralne jednačine.Introduction/purpose:Thispaper introducestheconceptofβ−F-weak contractionbyusingtheconceptsofF−weakcontractionandα−ψ− contraction. Methods: Theuseof theβ−F-weakcontractionprovessomefixed pointstheoremsintheframeworkofS−metricspaces. Results:TheobtainedresultsonfixedpointsinS−metricspacesgeneralizesomeknownresultsintheliterature. Conclusions:Theβ−F−weakcontractiongeneralizessomeimportant contractiontypesandexaminestheexistenceofafixedpointinS−metric spaces. Theresultsareusedtosolveanon-linearFredholmintegral equation

Fixed point theorems of generalized S - β - Ψ contractive type mappings

In this paper, we introduce the concept of generalised S - β - Ψ contractive type mappings. For these mappings we prove some fixed point theorems in the setting of S-metric space

Cyclic Relatively Nonexpansive Mappings with Respect to Orbits and Best Proximity Point Theorems

In this article, we introduce cyclic relatively nonexpansive mappings with respect to orbits and prove that every cyclic relatively nonexpansive mapping with respect to orbits T satisfying TA⊆B,TB⊆A has a best proximity point. We also prove that Mann’s iteration process for a noncyclic relatively nonexpansive mapping with respect to orbits converges to a fixed point. These relatively nonexpansive mappings with respect to orbits need not be continuous. Some illustrations are given in support of our results

Fixed Points of (<i>α</i>, <i>β</i>, <i>F</i>*) and (<i>α</i>, <i>β</i>, <i>F</i>**)-Weak Geraghty Contractions with an Application

This study aims to provide some new classes of (α,β,F*)-weak Geraghty contraction and (α,β,F**)-weak Geraghty contraction, which are self-generalized contractions on any metric space. Furthermore, we find that the mappings satisfying the definition of such contractions have a unique fixed point if the underlying space is complete. In addition, we provide an application showing the uniqueness of the solution of the two-point boundary value problem

On Generalized Rational α−Geraghty Contraction Mappings in G−Metric Spaces

In this paper, we discuss about various generalizations of α−admissible mappings. Furthermore, we extend the concept of α−admissible to generalize rational α−Geraghty contraction in G−metric space. With this new contraction mapping, we establish some fixed-point theorems in G−metric space. The obtained result is verified with an example

Remarks on α,β-Admissible Mappings and Fixed Points under Z-Contraction Mappings

In this paper, we discuss about different types of α,β-admissible mappings and introduce some new α,β-contraction-type mappings under simulation function. Furthermore, we present the definition of S-metric-like space and its topological properties. Some fixed point theorems in this space are established, proved, and verified with examples

Sufficient optimality conditions and duality for nonsmooth multiobjective optimization problems via higher order strong convexity

In this paper, we define some new generalizations of strongly convex functions of order m for locally Lipschitz functions using Clarke subdifferential. Suitable examples illustrating the non emptiness of the newly defined classes of functions and their relationships with classical notions of pseudoconvexity and quasiconvexity are provided. These generalizations are then employed to establish sufficient optimality conditions for a nonsmooth multiobjective optimization problem involving support functions of compact convex sets. Furthermore, we formulate a mixed type dual model for the primal problem and establish weak and strong duality theorems using the notion of strict efficiency of order m. The results presented in this paper extend and unify several known results from the literature to a more general class of functions as well as optimization problems