jQuery("#carousel").owlCarousel({
       ...
    navigation : true,
    navigationText : ["",""],
     ....
});

owl.carousel.css
owl.theme.default.css
jquery-3.1.1.min.js
owl.carousel.js

$('.owl-carousel').owlCarousel({
    loop:true,
    margin:10,
    nav:true,
    responsive:{
        0:{
            items:1
        },
        600:{
            items:3
        },
        1000:{
            items:5
        }
    }
})

navText : ["",""],

$('.owl-carousel').owlCarousel({
    loop:true,
    margin:10,
    nav:true,
    navText : ["",""],
    responsive:{
        0:{
            items:1
        },
        600:{
            items:3
        },
        1000:{
            items:5
        }
    }
})

.owl-prev{
          background-image: url("back.png");
          background-size: cover;
          width: 100px;
          height: 100px;
        }
        .owl-next{
          background-image: url("next.png");
          background-size: cover;
          width: 100px;
          height: 100px;
        }

background: #D6D6D6;

background-color: #D6D6D6;

background: #869791;

background-color: #869791;