CJM celebrates 25 years of publication of its new series

Author: Vasile Berinde

Abstract: This year, Carpathian Journal of Mathematics (CJM) reaches an important milestone - 25 years of
publication of its new series. Following an already well established tradition of marking the main anniversary moments of the journal by an editorial, see [Berinde, V., Anniversary: Ten years of publication of the new series of Buletin È˜tiinÈ›ific, Bul. È˜tiinÈ›. Univ. Baia Mare, Ser. B., MatematicÄƒ-InformaticÄƒ, 16 (2000), No. 1, iâ€“ii] and [Berinde, V., Carpathian Journal of Mathematics: Celebrating 20 years of publication of the new series, Carpathian J. Math., 26 (2010), No. 2, iâ€“vi], it is the main aim of this note to present a detailed account of what has been achieved since the previous anniversary editorial written five years ago.

Systems of variational relations with lower semicontinuous set-valued mappings

Author: Mircea Balaj

Abstract: In this paper, we use fixed point techniques to establish existence criteria of the solution for a system of two variational relations with lower semicontinuous set-valued mappings. PDF |

A constructive approach to coupled fixed point theorems in metric spaces

Author: Vasile Berinde / Mădălina Păcurar

Abstract: In this paper we establish the existence and uniqueness of a coupled fixed point for operators $F:X \times X \rightarrow X$ satisfying a new type of contractive condition, which is weaker than all the corresponding ones studied in literature so far. We also provide constructive features to our coupled fixed point results by proving that the unique coupled fixed point of $F$ can be approximated by means of two distinct iterative methods: a Picard type iterative method of the form $x_{n+1}=F(x_n,x_n),\,n\geq 0$, with $x_0\in X$, as well as a two step iterative method of the form $y_{n+1}=F(y_{n-1}, y_n),\,n\geq 0$, with $y_0,y_1 \in X$. We also give appropriate error estimates for both iterative methods.
Essentially we point out that all coupled fixed point theorems existing in literature, that establish the existence and uniqueness of a coupled fixed point with equal components, could be derived in a much more simpler manner. PDF |

Fixed point theorems for cyclic non-self single-valued almost contractions

Author: Vasile Berinde / Mihaela Ancuța Petric

Abstract: Let $X$ be a Banach space, $A$ and $B$ two non-empty closed subsets of $X$ and let $T:A\cup B\to X$ be an operator. We define the notion of cyclic non-self almost contraction and we give a corresponding fixed point theorem. PDF |

Fixed point theorems for Zamfirescu mappings in metric spaces endowed with a graph

Author: Florin Bojor / Magnolia Tilca

Abstract: Let $\left( {X,d} \right)$ be a metric space endowed
with a graph $G$ such that the set $V\left( G \right)$ of vertices of $G$ coincides with $X$. We define the notion of G-Zamfirescu maps and obtain a fixed point theorem for such mappings. This extends and subsumes many recent results which were obtained for mappings on metric spaces endowed with a graph and for cyclic operators. PDF |

Common fixed points for an uncountable family of weakly contractive operators

Author: Parin Chaipunya / Poom Kumam

Abstract: In this paper, we consider some behavior concerning common fixed points of an uncountable family of operators. We apply here the concept of circular metric spaces, and the operators are assumed to satisfy different rates of weak contractivity. We show under certain assumptions that weakly contractive family have some strong relationships to its common selector in terms of their fixed points. PDF |

Fixed points for mappings defined on generalized gauge spaces

Author: Mitrofan M. Choban

Abstract: In this article, the distinct classes of continuous pseudo-gauge structures and pseudometrics
(perfect, quasi-perfect, sequentially complete)
are defined and studied in depth.
The conditions under which the set of fixed points of a given mapping of a space with concrete
pseudo-gauge structure is non-empty are determined.
Some examples are proposed. PDF |

Common fixed points of two finite families of nonexpansive mappings
by iterations

Author: Hafiz Fukhar-ud-din

Abstract: We study a Mann type iterative scheme for two finite families of nonexpansive mappings and establish $\triangle -$ convergence and strong convergence theorems. The obtained results are
applicable in uniformly convex Banach spaces (linear domain) and CAT (0)
spaces (nonlinear domain) simultaneously. PDF |

On a generalized coupled fixed point theorem in $\mathcal{C}[0,1]$ and its application to a class of coupled systems of functional-integral equations

Author: J. Harjani / J. Rocha / K. Sadarangani

Abstract: In this paper, we present a result about the existence of a generalized coupled fixed point in the space $\mathcal{C}[0,1]$. Moreover, as an application of the result, we study the problem of existence and uniqueness of solution in $\mathcal{C}[0,1]$ for a general system of nonlinear functional-integral equations with maximum. PDF |

Some fixed points results on Branciari metric spaces via implicit functions

Author: Erdal Karapinar

Abstract: In this paper, we introduce the notion of $\alpha$-implicit contractive mapping of integral type in the context of Branciari metric spaces. The results of this paper, generalize and improve several results on the topic in literature. We give an example to illustrate our results. PDF |

A general convergence theorem for multiple-set split feasibility problem in Hilbert spaces

Author: Abdul Rahim Khan / Mujahid Abbas / Yekini Shehu

Abstract: We establish strong convergence result of split feasibility problem for a family of \linebreak quasi-nonexpansive multi-valued mappings and a total asymptotically strict pseudo-contractive mapping in infinite dimensional Hilbert spaces. PDF |

Common best proximity points for proximity commuting mapping with Geraghty's functions

Author: Poom Kumam / Chirasak Mongkolkeha

Abstract: In this paper, we prove new common best proximity point theorems for proximity commuting mapping by using concept of Geraghty's theorem in complete metric spaces. Our results improve and extend recent result of Sadiq Basha [Basha, S. S., Common best proximity points: global minimization of multi-objective functions, J. Glob Optim, 54 (2012), No. 2, 367-373] and some results in the literature. PDF |

On the theory of fixed point theorems for convex contraction mappings

Author: Viorica Mureșan / Anton S. Mureșan

Abstract: Based on the concepts and problems introduced in [Rus, I. A., The theory of a metrical fixed point theorem: theoretical and applicative relevances, Fixed Point Theory, 9 (2008), No. 2, 541--559], in the present paper we consider the theory of some fixed point theorems for convex contraction mappings. We give some results on the following aspects: data
dependence of fixed points; sequences of operators and fixed points; well-posedness of a fixed point problem; limit shadowing property and Ulam-Hyers stability for fixed point equations. PDF |

Fixed point theorems for correspondences with properties weaker than lower semicontinuity

Author: Monica Patriche

Abstract: In this paper, we study existence of fixed points for correspondences having weak continuity properties. The obtained results extend or improve the corresponding results present in literature. We use continuous selection technique and also well-known KKM principle in order to establish our fixed point theorems. PDF |

A new type of contractions that characterize metric completeness

Author: Ovidiu Popescu

Abstract: We prove that a new type of contractions characterizes the metric completeness of the underlying space. We also discuss the Meir-Keeler fixed point theorem. PDF |

Some fixed point theorems via partial order relations without the monotone property

Author: Warut Saksirikun / Narin Petrot

Abstract: The main aim of this paper is to consider some fixed point theorems via a partial order relation in complete metric spaces, when the considered mapping may not satisfy the monotonic properties. Furthermore, we also obtain some couple fixed point theorems, which can be viewed as an extension of a result that was presented in [V. Berinde, Generalized coupled fixed point theorems for mixed monotone mappings in partially ordered metric spaces, Nonlinear Anal., 74 (2011), 7347--7355]. PDF |

A new approach to $\alpha$-$\psi$-contractive mappings and generalized Ulam-Hyers stability, well-posedness and limit shadowing results

Author: Wutiphol Sintunavarat

Abstract: In this paper, we introduce the new concept of weakly $\alpha$-admissible mapping
and give example to show that our concept is different from the concept corresponding existing in the literature. We also establish fixed point theorems by using such concept along with $\alpha$-$\psi$-contractive condition and give some example which support our main result while previous results in literature are not applicable. Moreover, we study the generalized Ulam-Hyers stability, the well-posedness and the limit shadowing for fixed point problems satisfy our conditions. PDF |

Abstract: Jleli and Samet gave a new
generalization of the Banach contraction principle in the setting of
Branciari metric spaces [Jleli, M. and Samet, B., A new generalization of the Banach contraction principle}, J. Inequal. Appl., 2014:38 (2014)]. The purpose of this paper
is to study the existence of fixed points for multivalued mappings,
under a similar contractive condition, in the setting of complete
metric spaces. Some examples are provided to illustrate the new theory. PDF |