Parin Chaipunya

Geraghty-type theorems in modular metric spaces with an application to partial differential equation

In this article, we prove some fixed point theorems of Geraghty-type concerning the existence and uniqueness of fixed points under the setting of modular metric spaces. Also, we give an application of our main results to establish the existence and uniqueness of a solution to a nonhomogeneous linear parabolic partial differential equation in the last section.Mathematics Subject Classification (2010): 47H10, 54H25, 35K15.

Fixed-Point Theorems for Multivalued Mappings in Modular Metric Spaces

We give some initial properties of a subset of modular metric spaces and introduce some fixed-point theorems for multivalued mappings under the setting of contraction type. An appropriate example is as well provided. The stability of fixed points in our main theorems is also studied.

On P-contractions in ordered metric spaces

In this paper, we introduced a new type of a contractive condition defined on an ordered space, namely a P Open image in new window-contraction, which generalizes the weak contraction. We also proved some fixed point theorems for such a condition in ordered metric spaces. A supporting example of our results is provided in the last part of our paper as well.In this paper, we introduced a new type of a contractive condition defined on an ordered space, namely a P-contraction, which generalizes the weak contraction. We also proved some fixed point theorems for such a condition in ordered metric spaces. A supporting example of our results is provided in the last part of our paper as well.MSC:06A05, 06A06, 47H09, 47H10, 54H25.

On the Generalized Ulam-Hyers-Rassias Stability of Quadratic Mappings in Modular Spaces without -Conditions

We approach the generalized Ulam-Hyers-Rassias (briefly, UHR) stability of quadratic functional equations via the extensive studies of fixed point theory. Our results are obtained in the framework of modular spaces whose modulars are lower semicontinuous (briefly, lsc) but do not satisfy any relatives of -conditions.

Topological aspects of circular metric spaces and some observations on the KKM property towards quasi-equilibrium problems

The main purpose of this paper is to study some topological nature of circular metric spaces and deduce some fixed point theorems for maps satisfying the KKM property. We also investigate the solvability of a variant of a quasi-equilibrium problem as an application.MSC:54E35, 54H25.

On the Distance between Three Arbitrary Points

We point out some equivalence between the results in (Sedghi et al., 2012) and (Khamsi, 2010). Then, we introduce the notion of a general distance between three arbitrary points and study some of its properties. In the final section, some fixed point results are proposed.

On -contractions in ordered metric spaces

In this paper, we introduced a new type of a contractive condition defined on an ordered space, namely a P Open image in new window-contraction, which generalizes the weak contraction. We also proved some fixed point theorems for such a condition in ordered metric spaces. A supporting example of our results is provided in the last part of our paper as well.In this paper, we introduced a new type of a contractive condition defined on an ordered space, namely a P-contraction, which generalizes the weak contraction. We also proved some fixed point theorems for such a condition in ordered metric spaces. A supporting example of our results is provided in the last part of our paper as well.MSC:06A05, 06A06, 47H09, 47H10, 54H25.

On the proximal point method in Hadamard spaces

Abstract Proximal point method is one of the most influential procedure in solving nonlinear variational problems. It has recently been introduced in Hadamard spaces for solving convex optimization, and later for variational inequalities. In this paper, we study the general proximal point method for finding a zero point of a maximal monotone set-valued vector field defined on a Hadamard space and valued in its dual. We also give the relation between the maximality and Minty’s surjectivity condition, which is essential for the proximal point method to be well-defined. By exploring the properties of monotonicity and the surjectivity condition, we were able to show under mild assumptions that the proximal point method converges weakly to a zero point. Additionally, by taking into account the metric subregularity, we obtained the local strong convergence in linear and super-linear rates.

Some analogies of the Banach contraction principle in fuzzy modular spaces.

We established some theorems under the aim of deriving variants of the Banach contraction principle, using the classes of inner contractions and outer contractions, on the structure of fuzzy modular spaces.

New methods of construction of cartesian authentication codes from geometries over finite commutative rings

Abstract In this paper, we construct some cartesian authentication codes from geometries over finite commutative rings. We only assume the uniform probability distribution over the set of encoding rules in order to be able to compute the probabilities of successful impersonation attack and substitution attack. Our methods are comfortable and secure for users, i.e., our encoding rules reduce the probabilities of successful impersonation attack and substitution attack.