In the present paper, we introduce the notion of a generalized partial metric space which is an extension of the partial metric space due to S. G. Matthews (Partial metric topology, Papers on general topology and applications, Ann. New York Acad. Sci.,728 (1994), 183-197). We investigate some basic properties of the generalized partial metric spaces and establish some new fixed point theorems for linear and non-linear contraction on such spaces.
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Three variants of R-weakly commuting mappings in the realm of uniform spaces are defined. Examples are included to reflect upon the distinctiveness of the notions so defined. Common fixed point theorems concerning these variants of R-weakly commuting mappings in the framework of uniform spaces are obtained. This generalizes several known results in the literature including those of Granas and Dugundji [3], Tarafdar [12] and others. Moreover, as a bi-product we obtain several common fixed point theorems which are well in contrast with a common fixed point theorem of Jungck [4] who proved the same for commuting mappings.
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A pro.babilistic versuion of Meir and Keeler fixed point theorem and a generalization of Park' s coincidence theorem in random normed spaces are presented.
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This paper deals with the study of existence and uniqueness criteria for initial and boundary value problems associated with fuzzy differential equations of first and second order with the help of a modified Lipschitz condition.
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In this paper, some results on the equi-boundedness of solutions, the stability of the zero and the existence of positive periodic solutions of nonlinear difference equation with variable delay (…) are obtained.
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