NEW BOUNDS FOR SOME GENERALIZED EULER-TYPE CONSTANTS AND THEIR ACHIEVEMENTS

Subject Areas : Analyze

Negar Mohammadi ¹ , Mohammad Hadi Hooshmand ^{2 *}

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Received: 2022-05-15 Accepted : 2023-01-13 Published : 2024-09-25

Keywords: تابع جمع بند حدی, جمع پذیری حدی توابع حقیقی, ثابت نوع اویلر, نابرابری های مربوط به توابع,

Abstract :

We deal with some generalizations of Euler-Type constants that are motivated by derivatives of limit summand functions. In order to study the derivative of the summand functions, the second author had faced a functional sequence leading him to a generalization of the Euler-type constants. In this paper, we give some new bounds for such generalized Euler type constants and state some related results and inequalities. As a result of the topic, we obtain upper and lower bounds for a series of the sequence f'(j) (obtained from the derivatives of f at positive integer points, if f is differentiable) for all real functions with certain properties. The obtained results can be applied to a wide range of special functions. Finally, we state some of their applications for several special functions, that one of them is an inequality for the inverse function of the tangent function (for all positive integers m) .