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Article Citation - WoS: 3Uniqueness 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; MathematicsThe 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.Article Citation - WoS: 2Citation - Scopus: 2Spectrum of the q-schrodinger Equation by Means of the Variational Method Based on the Discrete q-hermite I Polynomials(World Scientific Publ Co Pte Ltd, 2021) Turan, Mehmet; Adiguzel, Rezan Sevinik; Calisir, Ayse DoganIn this work, the q-Schrodinger equations with symmetric polynomial potentials are considered. The spectrum of the model is obtained for several values of q, and the limiting case as q -> 1 is considered. The Rayleigh-Ritz variational method is adopted to the system. The discrete q-Hermite I polynomials are handled as basis in this method. Furthermore, the following potentials with numerous results are presented as applications: q-harmonic, purely q-quartic and q-quartic oscillators. It is also shown that the obtained results confirm the ones that exist in the literature for the continuous case.
