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Article Citation - WoS: 8Citation - Scopus: 9Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem Revisited(Taylor & Francis Ltd, 2021) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayThe extension of the Schwarz representation formula to simply connected domains with harmonic Green function and its polyanalytic generalization is not valid in general. They do hold only for certain domains.Article Citation - WoS: 10Citation - Scopus: 10Av Bitsadze's Observation on Bianalytic Functions and the Schwarz Problem(Taylor & Francis Ltd, 2019) Aksoy, Umit; Begehr, Heinrich; Celebi, A. OkayAccording to an observation of A.V. Bitsadze from 1948 the Dirichlet problem for bianalytic functions is ill-posed. A natural boundary condition for the polyanalytic operator, however, is the Schwarz condition. An integral representation for the solutions in the unit disc to the inhomogeneous polyanalytic equation satisfying Schwarz boundary conditions is known. This representation is extended here to any simply connected plane domain having a harmonic Green function. Some other boundary value problems are investigated with some Dirichlet and Neumann conditions illuminating that just the Schwarz problem is a natural boundary condition for the Bitsadze operator.Editorial Special Issue: in Honour of Professor A. Okay Celebi on the Occasion of His 70th Birthday Preface(Taylor & Francis Ltd, 2013) Aksoy, Umit[No Abstract Available]Article Citation - WoS: 1Citation - Scopus: 4Fixed Point Theorems for Mappings With a Contractive Iterate at a Point in Modular Metric Spaces(House Book Science-casa Cartii Stiinta, 2022) Karapinar, Erdal; Aksoy, Umit; Fulga, Andreea; Erhan, Inci M.In this manuscript, we introduce two new types of contraction, namely, w-contraction and strong Sehgal w-contraction, in the framework of modular metric spaces. We indicate that under certain assumptions, such mappings possess a unique fixed point. For the sake of completeness, we consider examples and an application to matrix equations.Article Citation - WoS: 68FIXED 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.
