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## Approximations of ternary Jordan homomorphisms and derivations in multi-C ∗ ternary algebras

### Acta Mathematica Hungarica (2012-01-01) 134: 99-114 , January 01, 2012

Using fixed point methods, we prove the generalized Hyers–Ulam stability of homomorphisms in multi-*C*^{∗} ternary algebras and of derivations on multi-*C*^{∗} ternary algebras for the additive functional equation
$$\sum_{i=1}^{m}f \bigg(mx_i+\sum_{j=1,\ j\ne i}^{m}x_j\bigg)+ f\bigg(\sum_{i=1}^{m}x_i\bigg)= 2f\bigg(\sum_{i=1}^{m}mx_i\bigg) \quad (m\in {\mathbb{N}},\ m\geqq2).$$

## Solvability of a System of Vector Equilibrium Problems Involving Topological Pseudomonotonicity

### Bulletin of the Malaysian Mathematical Sciences Society (2016-10-01) 39: 1379-1390 , October 01, 2016

In this paper, we study the solvability of a system of vector equilibrium problems. We extend the concept of topological pseudomonotonicity to a family of mappings. We prove existence results for the system of vector equilibrium problems under topological pseudomonotonicity conditions by the Kakutani–Fan–Glicksberg fixed point theorem. As applications, we obtain existence results for systems of equilibrium problems under topological pseudomonotonicity conditions.

## On a class of nonhomogeneous fractional quasilinear equations in $${\mathbb{R}^n}$$ R n with exponential growth

### Nonlinear Differential Equations and Applications NoDEA (2015-08-01) 22: 499-511 , August 01, 2015

This paper examines a class of nonlocal equations involving the fractional *p*-Laplacian, where the nonlinear term is assumed to have exponential growth. More specifically, by using a suitable Trudinger–Moser inequality for fractional Sobolev spaces, we establish the existence of weak solutions for these equations.

## A generalization of set-valued Prešić–Reich type contractions in ultrametric spaces with applications

### Journal of Fixed Point Theory and Applications (2016-10-24): 1-17 , October 24, 2016

In this paper, we study the existence and uniqueness of coincidence and common fixed point of a set-valued and a single-valued mapping satisfying generalized set-valued Prešić–Reich type contractive condition in ultrametric spaces without the property of completeness. As an application, the well-posedness of a common fixed point problem is proved. An example is given to illustrate our results. Our results generalize and extend the results of Prešić–Reich in the context of ultrametric spaces.

## An altering distance function in fuzzy metric fixed point theorems

### Fixed Point Theory and Applications (2015-05-14) 2015: 1-19 , May 14, 2015

The aim of this paper is to improve conditions proposed in recently published fixed point results for complete and compact fuzzy metric spaces (Ćirić in Chaos Solitons Fractals 42:146-154, 2009; Shen *et al.* in Appl. Math. Lett. 25:138-141, 2012). For this purpose, the altering distance functions are used. Moreover, in some of the results presented the class of *t*-norms is extended by using the theory of countable extensions of *t*-norms. The mentioned generalizations are illustrated by examples.

## Fixed point theorems via generalized $$\varvec{F}$$ F -contractions with applications to functional equations occurring in dynamic programming

### Journal of Fixed Point Theory and Applications (2017-06-01) 19: 1453-1479 , June 01, 2017

The purpose of this paper is threefold. Firstly, recognizing the concept of Piri and Kumam (Fixed Point Theor Appl 210, 2014), we define generalized *F*-contractive mappings in the framework of *G*-metric spaces and by employing this, some fixed point theorems in the structure of *G*-metric spaces are established that can not be obtained from the existing results in the context of allied metric spaces and do not meet the remarks of Samet et al. (Int J Anal. Article ID 917158, 2013) and Jleli et al. (Fixed Point Theor Appl 210, 2012). Infact, we utilize the pattern, mentioned in Karapinar and Agrawal (Fixed Point Theor Appl 154, 2013), a counter paper to remarks of Samet et al. (Int J Anal. Article ID 917158, 2013) and Jleli et al. (Fixed Point Theor Appl 210, 2012). Secondly, in the setting of *G*-metric spaces, certain fixed point results for integral inequalities under generalized *F*-contraction are presented. Finally, as an application, our results are utilized to establish the existence and uniqueness of solution the equations arising in Oscillation of a spring. In the sequel, another application is given to set-up the existence and uniqueness of solution of functional equations occurring in dynamic programming. Our investigations are also authenticated with the aid of some appropriate and innovative examples.

## Proximal point algorithms involving fixed points of nonexpansive mappings in CAT ( 0 ) $\operatorname{CAT}(0)$ spaces

### Fixed Point Theory and Applications (2015-12-10) 2015: 1-13 , December 10, 2015

In this paper, we introduce a new modified proximal point algorithm involving fixed point iterates of nonexpansive mappings in $\operatorname{CAT}(0)$ spaces and prove that the sequence generated by our iterative process converges to a minimizer of a convex function and a fixed point of mappings.

## A fixed point theorem for Meir-Keeler type contraction via Gupta-Saxena expression

### Fixed Point Theory and Applications (2015-07-15) 2015: 1-9 , July 15, 2015

In this paper, following the idea of Samet *et al.* (J. Nonlinear. Sci. Appl. 6:162-169, 2013), we establish a new fixed point theorem for a Meir-Keeler type contraction via Gupta-Saxena rational expression which enables us to extend and generalize their main result (Gupta and Saxena in Math. Stud. 52:156-158, 1984). As an application we derive some fixed points of mappings of integral type.

## Common fixed point theorems under generalized $$\mathcal {W}$$ W -weakly contractive condition in ordered orbitally complete metric spaces

### Afrika Matematika (2016-03-01) 27: 297-312 , March 01, 2016

We propose common fixed point results for two pairs of partially weakly increasing mappings in an ordered orbitally complete metric space under a generalized rational-type $$\mathcal {W}$$ -weakly contractive condition. As an application, an existence result for certain systems of integral equations is presented.

## Nonlinear integral equations with new admissibility types in b-metric spaces

### Journal of Fixed Point Theory and Applications (2016-06-01) 18: 397-416 , June 01, 2016

In this paper, we aim to introduce new types of *α*-admissibility in the framework of *b*-metric spaces. Some examples to show the independently of each type of α-admissibility are given. Using these concepts, fixed point theorems satisfying generalized weak contractive condition in the setting of *b*-metric spaces are established. We furnish an illustrative example to demonstrate the validity of the hypotheses and the degree of utility of our results. As an application, we discuss the existence of a solution for the following nonlinear integral equation:
$$x(c) = \phi (c) + {\int _{a}^{b}} K(c, r, x(r)) dr,$$
where
$${a, b \in {\mathbb{R}}}$$
such that
$${a < b, x \in C[a, b]}$$
(the set of all continuous functions from [*a*, *b*] into
$${{\mathbb{R}}}$$
),
$${\phi : [a, b] \rightarrow {\mathbb{R}}}$$
and
$${K : [a, b] \times [a, b] \times {\mathbb{R}} \rightarrow {\mathbb{R}}}$$
are given mappings.