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ON A GENERALIZED α-ADMISSIBLE RATIONAL TYPE CONTRACTIVE MAPPING
(Yokohama Publ, 2016) Erhan, Inci M.; Kir, Mehmet
Recently, many generalized contractive conditions which involve rational contractive inequalities have been introduced in the context of partially ordered metric spaces. In this paper, we aim to give a generalized rational contractive condition which involves some of these results without need of extra restrictions.
Citation - WoS: 68
FIXED POINTS OF GENERALIZED α-ADMISSIBLE CONTRACTIONS ON b-METRIC SPACES WITH AN APPLICATION TO BOUNDARY VALUE PROBLEMS
(Yokohama Publ, 2016) Aksoy, Umit; Karapinar, Erdal; Erhan, Inci M.
A general class of alpha-admissible contractions defined via (b)-comparison functions on b-metric spaces is discussed. Existence and uniqueness of the fixed point for this class of contractions is studied. Some consequences are presented. The results are employed in the discussion of existence and uniqueness of solutions of first order boundary value problems for ordinary differential equations.
On the Existence and Uniqueness of Solutions of Fractional Dynamic Equations On Time Scales
(Yokohama Publ, 2022) Erhan, Inci M.
The existence and uniqueness of solutions of Cauchy problem for a nonlinear Caputo fractional dynamic equation of arbitrary order alpha > 0 is studied. The problem is treated as a fixed point problem posed on a b-metric space. A numerical example is presented to support the theoretical results.