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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: 3Citation - Scopus: 3On the Fixed Points of Iterative Contractive Mappings Defined Via Implicit Relation(Taylor & Francis Ltd, 2021) Aksoy, Umit; Erhan, Inci M.; Fulga, Andreea; Karapinar, ErdalIn this paper, we consider an implicit relation to generalize iterative fixed point results in the literature in the context of metric spaces. We conclude that several existing results are immediate consequences of our main results.Article Dirichlet-Type Problems for n-poisson Equation in Clifford Analysis(Taylor & Francis Ltd, 2022) Aksoy, Umit; Celebi, A. OkayIterated Dirichlet problem, also called as Riquier or Navier problem, and polyharmonic Dirichlet problem are studied for n-Poisson equation in Clifford analysis using iterated polyharmonic Green function and polyharmonic Green-Almansi type function appropriate for the boundary conditions of the problems.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]
