HERMITE-HADAMARD TYPE INEQUALITIES FOR CONFORMABLE INTEGRALS VIA η-CONVEX FUNCTIONS

Many recent results have been. This inequality has many applications in the area of pure and applied mathematics. In this paper, our main aim is to give results for conformable integral version of Hermite-Hadamard inequality for η-convex functions. First, we prove an identity associated with the Hermite-Hadamard inequality for conformable integrals using η-convex functions. By using this identity and η-convexity of function and some well-known inequalities, we obtain several results for the inequality

ON PARAMETRIZED HERMITE-HADAMARD TYPE INEQUALITIES

In recent years, many results have been devoted to the well-known Hermite-Hadamard inequality. This inequality has many applications in the area of pure and applied mathematics. In this paper, our main aim is to give a parametrized inequality of the Hermite-Hadamard type and its applications to f-divergence measures and means.First, we prove the identity associated with the right side of the Hermite-Hadamard inequality. By using this identity, the convexity of the function and some well-known inequalities, we obtain several results for the inequality. The inequalities derived here also point out some known results as their special cases

Conformable Integral Inequalities of the Hermite-Hadamard Type in terms of GG- and GA-Convexities

In the article, we present several conformable fractional integrals’ versions of the Hermite-Hadamard type inequalities for GG- and GA-convex functions and provide their applications in special bivariate means

Inequalities for Three Times Differentiable Functions

In this article, first we prove a new integral identity and present some general inequalities of Hadamard’s type for the functions whose third derivative are concave (convex). Second applications for special means and some new error estimates of the Midpoint formula are given

New Hermite-Hadamard Type Inequalities With Applications

In this manuscript, we have established two new integral identities connected with the left hand side of Hermite-Hadamard (H-H) inequality. By using these identities, we have obtained some new bounds for the Hadamard’s type inequalities. We have also presented applications for means and for some error estimates of the mid point formula

Hermite-Hadamard-Fejér Inequalities for Conformable Fractional Integrals via Preinvex Functions

In this paper, we present a Hermite-Hadamard-Fejér inequality for conformable fractional integrals by using symmetric preinvex functions. We also establish an identity associated with the right hand side of Hermite-Hadamard inequality for preinvex functions; then by using this identity and preinvexity of functions and some well-known inequalities, we find several new Hermite-Hadamard type inequalities for conformal fractional integrals

Generalization of Hermite-Hadamard Type Inequalities via Conformable Fractional Integrals

We establish a Hermite-Hadamard type identity and several new Hermite-Hadamard type inequalities for conformable fractional integrals and present their applications to special bivariate means

Robust and computationally efficient online image stabilisation framework based on adaptive dual motion vector integration

Image stabilisation aims to compensate and smoothen the effects of undesired trembling motion of cameras mounted on non‐static platforms. It becomes quite a challenging task in the case of moving platforms, such as ground vehicles, unmanned aerial vehicles, and handheld devices. Many satisfactory solutions to the image stabilisation problem are proposed in the recent literature, but most of these methods are not adaptable for handling a wide range of intentional motions with minimum lag, especially in real‐time scenarios. In this study, the authors propose an online two‐dimensional image stabilisation technique based on dual motion vector integration, which is a novel adaptive motion smoothing technique that employs an average length of motion vectors to estimate the intentional motion. The overall computational cost of the proposed system is significantly reduced by employing frame‐shaking judgment that only allows processing of jittering frames. Promising experimental results have been obtained on challenging videos obtained from hand‐held and vehicle‐mounted cameras which demonstrate the robustness and effectiveness of the proposed technique against feature point mismatching and presence of moving objects within the scene at a frame rate of 30 frames per second

Frequency of foot ulcers in people with type 2 diabetes, presenting to specialist diabetes clinic at a Tertiary Care Hospital, Lahore, Pakistan

Abstract Background Diabetic foot ulceration is a serious limb-threatening complication of diabetes. It is the common cause of hospital admissions and amputations. The objective of the study was to determine the prevalence of diabetic foot ulcers (DFU) and its association with age, gender, duration of diabetes, peripheral neuropathy (PN), peripheral arterial disease (PAD) and HbA1c. Methods A total of 1940 people (≥ 30 years of age) with type 2 diabetes coming to the Sakina Institute of Diabetes and Endocrine Research (specialist diabetes clinic) at Shalamar Hospital, Lahore, Pakistan, were recruited over a period of 1 year from January 2016 to January 2017. The foot ulcers were identified according to the University of Texas classification. PN was assessed by biothesiometer and PAD by ankle-brachial index (< 0.9). Body weight, height, body mass index (BMI), HbA1c and duration of diabetes were recorded. Results The prevalence of DFU was 7.02%, of which 4.5% of the ulcers were on the planter and 2.6% on the dorsal surface of the foot; 8.5% of the persons had bilateral foot ulcers and 0.4% subjects had Charcot deformity. There was significant association of foot ulcers with age, duration of diabetes, HbA1c, PN and PAD, whereas no association was observed with gender and BMI. PN and PAD were observed in 26.3 and 6.68% of people with diabetes respectively. Neuropathic ulcers and neuro-ischemic ulcers were identified in 74 and 19% of the study population. Logistic regression analysis revealed significant odds ratio for peripheral neuropathy 23.9 (95% confidence interval (5.41–105.6). Conclusions Peripheral neuropathy is the commonest cause of foot ulcers. An optimum control of blood glucose to prevent neuropathy and regular feet examination of every person with diabetes may go a long way in preventing foot ulceration