fixed-point theory

In this paper, we improve the previous results from fixed point theory related to four types of contractions: interpolative Kannan contraction, extended interpolative and Geraghty type contraction, interpolative Hardy-Rogers contraction and Wardowski F-contraction. The basis for our generalization is the results from ``Extended Interpolative Hardy-Rogers-Geraghty-Wardowski Contractions and an Application'' as well as ``On extended interpolative \'{C}iri\'{c}-Reich-Rus type F-contractions and an application''.

The main objective of this article is to introduce gradual normed Riesz spaces and their properties. In fact, by adding a property to gradual normed spaces as discussed in reference [20], we have defined the gradual Banach lattices. Next, we focus on the stability of the supremum-preserving functional equation in these spaces, utilizing the fixed-point theorem to examine the conditions ensuring stability. Also, we can verify the stability of various functional equations in these spaces.

This paper deals with the existence and exact controllability of a class of non-instantaneous impulsive stochastic integro-differential equations with nonlocal conditions in a Hilbert space under the assumption that the semigroup generated by the linear part is noncompact.  A set of sufficient conditions are generated using the stochastic analysis technique,   Kuratowskii's measure of non-compactness, a resolvent operator and a generalized Darbo's fixed point theorem to obtain existence and controllability results of mild solutions for the considered system. Examples are also given to illustrate the effectiveness of controllability results obtained.

‎In this paper‎, ‎‎a common zero of a finite family of monotone operators on Hadamard spaces is‎‎ approximated via Mann-type proximal point algorithm. Some applications in convex minimization and fixed point theory are also presented.

The essential purpose of this paper is to obtain the fixed point of different functions by using a modern repetitive method. We incorporate concepts suggested in the Bisection method and the Moth-Flame Optimization algorithm. This algorithm is more impressive for finding fixed point functions. We also implement this method for four functions and finally compare the current method with other methods such as ALO, MVO, SSA, SCA algorithms. the proposed method shows a decent functionality than the other four methods.

In this manuscript, we study the fractional-order SIRC epidemiological model for influenza A in the human population in the Caputo-Fabrizio sense. The existence and uniqueness of the solution of the proposed problem are established using fixed point theory. The local stability of both disease-free equilibrium and endemic equilibrium points is investigated. Using the three-step fractional Adams-Bashforth scheme, an iterative solution of our system is generated. In the numerical simulation, many plots are given for different values of the fractional order to check the stability of equilibrium points. Also, the effect of varying some parameters of the model was presented. Furthermore, we compared our numerical solutions with those using Caputo fractional derivative model via graphical representations. The obtained results show the efficiency and accuracy of our approach.

In this paper, we aim to study the Ulam-Hyers stability and Ulam-Hyers-Rassias stability of the fuzzy delay differential equation under some suitable conditions by the fixed point technique and successive approximation method. Moreover, we provide two illustrative examples of application of our results.

In this paper, we investigate the existence and uniqueness of solution for fractionalboundary value problem (FBVP) with the integral boundary conditions. We use the contraction mapping principle and Krasnoselskii’s fixed point theorem to obtain some new existence and uniqueness results.

We introduce variational inequality problems on 2-inner product spaces and prove several existence results for variational inequalities defined on closed convex sets. Also, the relation between variational inequality problems, best approximation problems and fixed point theory is studied.

The purpose of this work is to investigate the existence of fixed points of some mappings in fixed point theory by combining some important concepts which are F-weak contractions, multivalued mappings, integral transformations and α-admissible mappings. In fixed point theory, it is important to find fixed points of some classess under F- or F-weak contractions. Also multivalued mappings is the other important classes. Along with that, α-admissible mapping is a different approach in the fixed point theory. According to this method, a single or multivalued mapping does not have a fixed point in general. But, under some restriction on the mapping, a fixed point can be obtained. In this article, we combine four significant notions and also establish fixed point theorem for this mappings in complete metric spaces. Moreover, we give an example to show the interesting of our results according to earlier results in literature.The formula is not displayed correctly!