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Citation - WoS: 2
Uniqueness of Solution for Second Order Nonlinear q-difference Equations With Multi-Point and Integral Boundary Conditions
(Yokohama Publ, 2022) Adiguzel, Rezan Sevinik; Sevinik Adıgüzel, Rezan; Sevinik Adıgüzel, Rezan; Mathematics; Mathematics
The existence and uniqueness of the solution for the boundary value problem associated with nonlinear second-order q-difference equation is discussed by Banach contraction mapping theorem on b-metric spaces. The problem is converted to an integral equation and investigated via a fixed point problem for an integral operator. Existence and uniqueness conditions for a fixed point of the integral operator are obtained. Moreover, an example is introduced to support the main results.
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.