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    On a fekete–szegö problem associated with generalized telephone numbers
    (Multidisciplinary Digital Publishing Institute (MDPI), 2023) Breaz, Daniel; Wanas, Abbas Kareem; Sakar, Fethiye Müge; Aydoǧan, Seher Melike
    One of the important problems regarding coefficients of analytical functions (i.e., Fekete–Szegö inequality) was raised by Fekete and Szegö in 1933. The results of this research are dedicated to determine upper coefficient estimates and the Fekete–Szegö problem in the class (Formula presented.), which is defined by generalized telephone numbers. We also indicate some specific conditions and consequences of results found by us.
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    A study on the existence of numerical and analytical solutions for fractional integrodifferential equations in hilfer type with simulation
    (American Institute of Mathematical Sciences, 2023) George, Reny; Aydoǧan, Seher Melike; Sakar, Fethiye Müge; Ghaderi, Mehran; Rezapour, Shahram
    Previous studies have shown that fractional derivative operators have become an integral part of modeling natural and physical phenomena. During the progress and evolution of these operators, it has become clear to researchers that each of these operators has special capacities for investigating phenomena in engineering sciences, physics, biological mathematics, etc. Fixed point theory and its famous contractions have always served as useful tools in these studies. In this regard, in this work, we considered the Hilfer-type fractional operator to study the proposed integrodifferential equation. We have used the capabilities of measure theory and fixed point techniques to provide the required space to guarantee the existence of the solution. The Schauder and Arzela-Ascoli theorems play a fundamental role in the existence of solutions. Finally, we provided two examples with some graphical and numerical simulation to make our results more objective.
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    The yamaguchi–noshiro type of bi-univalent functions connected with the linear q-convolution operator
    (Multidisciplinary Digital Publishing Institute (MDPI), 2023) Breaz, Daniel; El-Deeb, Sheza M.; Aydoǧan, Seher Melike; Sakar, Fethiye Müge
    In the present paper, the authors introduce and investigate two new subclasses of the function class (Formula presented.) of bi-univalent analytic functions in an open unit disk (Formula presented.) connected with a linear q-convolution operator. The bounds on the coefficients (Formula presented.) and (Formula presented.) for the functions in these new subclasses of (Formula presented.) are obtained. Relevant connections of the results presented here with those obtained in earlier work are also pointed out.