0000000000713491
AUTHOR
B Samet
A fixed point theorem for uniformly locally contractive mappings in a C-chainable cone rectangular metric space
Recently, Azam, Arshad and Beg [ Banach contraction principle on cone rectangular metric spaces, Appl. Anal. Discrete Math. 2009] introduced the notion of cone rectangular metric spaces by replacing the triangular inequality of a cone metric space by a rectangular inequality. In this paper, we introduce the notion of c-chainable cone rectangular metric space and we establish a fixed point theorem for uniformly locally contractive mappings in such spaces. An example is given to illustrate our obtained result.
Comments on the paper "COINCIDENCE THEOREMS FOR SOME MULTIVALUED MAPPINGS" by B. E. RHOADES, S. L. SINGH AND CHITRA KULSHRESTHA
The aim of this note is to point out an error in the proof of Theorem 1 in the paper entitled “Coincidence theorems for some multivalued mappings” by B. E. Rhoades, S. L. Singh and Chitra Kulshrestha [Internat. J. Math. & Math. Sci., 7 (1984), 429-434], and to indicate a way to repair it.
From Caristi’s Theorem to Ekeland’s Variational Principle in ${0}_{\sigma }$ -Complete Metric-Like Spaces
We discuss the extension of some fundamental results in nonlinear analysis to the setting of ${0}_{\sigma }$ -complete metric-like spaces. Then, we show that these extensions can be obtained via the corresponding results in standard metric spaces.
Fixed point theorems for $\alpha$-$\psi$-contractive type mappings
In this paper, we introduce a new concept of $\alpha$-$\psi$-contractive type mappings and establish fixed point theorems for such mappings in complete metric spaces. Starting from the Banach contraction principle, the presented theorems extend, generalize and improve many existing results in the literature. Moreover, some examples and applications to ordinary differential equations are given here to illustrate the usability of the obtained results.
Special Issue on Ciric type fixed point theorems
Professor Ljubomir Ćirić was born on August 13, 1935 in Resnik, environmentof the Niš, in Serbia. Primary,secondary and university education Professor Ćirić received in Belgrade, where he completed his Mr Sci and his Dr Sci in 1969. His fields of specialization are Fixed point theory and Nonlinear analysis. He has been founder of different directions in the theory of fixed points, which and in today's time are in the full development. During the past 45 years, he has given significant contributions to these areas. We want point out that his works have been published and cited in prestigious international journals. Two of his work has been cited in the Web of Science over 560 times, each ove…
Optimization Problems via Best Proximity Point Analysis
Many problems arising in different areas of mathematics, such as optimization, variational analysis, and differential equations, can be modeled as equations of the form Tx=x, where T is a given mapping in the framework of a metric space. However, such equation does not necessarily possess a solution if T happens to be nonself-mapping. In such situations, one speculates to determine an approximate solution x (called a best proximity point) that is optimal in the sense that the distance between x and Tx is minimum. The aim of best proximity point analysis is to provide sufficient conditions that assure the existence and uniqueness of a best proximity point. This special issue is focused on th…