Fixed point results with applications to nonlinear fractional differential equations

The aim of this paper is to define a Berinde type ($\rho$, $\mu$)-$\vartheta$ contraction and establish some fixed point results for self mappings in the setting of complete metric spaces. We derive new fixed point results, which extend and improve some results in the literature. We also supply a non trivial example to support the obtained results. Finally, we investigate the existence of solutions for the nonlinear fractional differential equation

Some New Fuzzy Fixed Point Results with Applications

The aim of this article is to establish some fixed point results for fuzzy mappings and derive some corresponding multivalued mappings results of literature. For this purpose, we define some new and generalized contractions in the setting of b-metric spaces. As applications, we find solutions of integral inclusions by our obtained results.Deanship of Scientific Research (DSR), University of Jeddah, Jeddah. Grant No. UJ-02-007-ICGR

Generalized Fixed-Point Results for Almost (α,Fσ)-Contractions with Applications to Fredholm Integral Inclusions

The purpose of this article is to define almost ( α , F σ ) -contractions and establish some generalized fixed-point results for a new class of contractive conditions in the setting of complete metric spaces. In application, we apply our fixed-point theorem to prove the existence theorem for Fredholm integral inclusions ϖ ( t ) ∈ f ( t ) + ∫ 0 1 K ( t , s , x ( s ) ) ϑ s , t ∈ [ 0 , 1 ] where f ∈ C [ 0 , 1 ] is a given real-valued function and K : [ 0 , 1 ] × [ 0 , 1 ] × R → K c v ( R ) is a given multivalued operator, where K c v represents the family of nonempty compact and convex subsets of R and ϖ ∈ C [ 0 , 1 ] is the unknown function. We also provide a non-trivial example to show the significance of our main result

Common α-Fuzzy Fixed Point Results for F-Contractions with Applications

F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature

Common <i>α</i>-Fuzzy Fixed Point Results for <i>F</i>-Contractions with Applications

F-contractions have inspired a branch of metric fixed point theory committed to the generalization of the classical Banach contraction principle. The study of these contractions and α-fuzzy mappings in b-metric spaces was attempted timidly and was not successful. In this article, the main objective is to obtain common α-fuzzy fixed point results for F-contractions in b-metric spaces. Some multivalued fixed point results in the literature are derived as consequences of our main results. We also provide a non-trivial example to show the validity of our results. As applications, we investigate the solution for fuzzy initial value problems in the context of a generalized Hukuhara derivative. Our results generalize, improve and complement several developments from the existing literature

Fixed Point Theorems for Generalized (αβ-ψ)-Contractions in F -Metric Spaces with Applications

The purpose of this paper is to define generalized ( &alpha; &beta; - &psi; ) -contraction in the context of F -metric space and obtain some new fixed point results. As applications, we solve a nonlinear neutral differential equation with an unbounded delay &thetasym; / ( &iota; ) = &minus; &rho; 1 ( &iota; ) &thetasym; ( &iota; ) + &rho; 2 ( &iota; ) L ( &thetasym; ( &iota; &minus; &sigmaf; ( &iota; ) ) ) + &rho; 3 ( &iota; ) &thetasym; / ( &iota; &minus; &sigmaf; ( &iota; ) ) , where &rho; 1 ( &iota; ) , &rho; 2 ( &iota; ) are continuous, &rho; 3 ( &iota; ) is continuously differentiable and &sigmaf; ( &iota; ) &gt; 0 , for all &iota; &isin; R and is twice continuously differentiable

One-local retract and common fixed point in modular function spaces

In this paper, we introduce and study the concept of one-local retract in modular function spaces. In particular, we prove that any commutative family of ρ-nonexpansive mappings defined on a nonempty, ρ-closed and ρ-bounded subset of a modular function space has a common fixed point provided its convexity structure of admissible subsets is compact and normal

Fixed Point Results for Perov–Ćirić–Prešić-Type Θ-Contractions with Applications

The aim of this paper is to introduce the notion of Perov–Ćirić–Prešić-type Θ-contractions and to obtain some generalized fixed point theorems in the setting of vector-valued metric spaces. We derive some fixed point results as consequences of our main results. A nontrivial example is also provided to support the validity of our established results. As an application, we investigate the solution of a semilinear operator system in Banach space

Fixed point theory, variational analysis, and optimization

""There is a real need for this book. It is useful for people who work in areas of nonlinear analysis, optimization theory, variational inequalities, and mathematical economics.""-Nan-Jing Huang, Sichuan University, Chengdu, People's Republic of China</P