Browsing by Author "Dragomir, Sever"

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    An extension of trapezoid inequality to the complex integral
    (Ankara Universitesi, 2021) Dragomir, Sever; Other; Other
    In this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity | ( v − u ) f ( u ) + ( w − v ) f ( w ) − ∫ γ f ( z ) d z | under the assumptions that γ is a smooth path parametrized by z ( t ) , t ∈ [ a , b ] , u = z ( a ) , v = z ( x ) with x ∈ ( a , b ) and w = z ( b ) while f is holomorphic in G , an open domain and γ ∈ G . An application for circular paths is also given.
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    Further inequalities for the generalized k-g-fractional integrals of functions with bounded variation
    (Ankara Üniversitesi Fen Fakültesi, 2020-06-30) Dragomir, Sever; Other; Other
    Let g be a strictly increasing function on (a,b), having a continuous derivative g′ on (a,b). For the Lebesgue integrable function f:(a,b)→C, we define the k-g-left-sided fractional integral of f by S_{k,g,a+}f(x)=∫_{a}^{x}k(g(x)-g(t))g′(t)f(t)dt, x∈(a,b] and the k-g-right-sided fractional integral of f by S_{k,g,b-}f(x)=∫_{x}^{b}k(g(t)-g(x))g′(t)f(t)dt, x∈[a,b), where the kernel k is defined either on (0,∞) or on [0,∞) with complex values and integrable on any finite subinterval. In this paper we establish some new inequalities for the k-g-fractional integrals of functions of bounded variation.Examples for the generalized left- and right-sided Riemann-Liouville fractional integrals of a function f with respect to another function g and a general exponential fractional integral are also provided.